One-Dimensional Quaternion Fourier Transform with Application to Probability Theory
The Fourier transform occupies a central place in applied mathematics, statistics, computer sciences, and engineering. In this work, we introduce the one-dimensional quaternion Fourier transform, which is a generalization of the Fourier transform. We derive the conjugate symmetry of the one-dimensio...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/4/815 |
| _version_ | 1797603419735719936 |
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| author | Wahyuni Ekasasmita Mawardi Bahri Nasrullah Bachtiar Amran Rahim Muhammad Nur |
| author_facet | Wahyuni Ekasasmita Mawardi Bahri Nasrullah Bachtiar Amran Rahim Muhammad Nur |
| author_sort | Wahyuni Ekasasmita |
| collection | DOAJ |
| description | The Fourier transform occupies a central place in applied mathematics, statistics, computer sciences, and engineering. In this work, we introduce the one-dimensional quaternion Fourier transform, which is a generalization of the Fourier transform. We derive the conjugate symmetry of the one-dimensional quaternion Fourier transform for a real signal. We also collect other properties, such as the derivative and Parseval’s formula. We finally study the application of this transformation in probability theory. |
| first_indexed | 2024-03-11T04:28:54Z |
| format | Article |
| id | doaj.art-3eb84c2e30994d2da3832abfaa1b96ea |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T04:28:54Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-3eb84c2e30994d2da3832abfaa1b96ea2023-11-17T21:33:08ZengMDPI AGSymmetry2073-89942023-03-0115481510.3390/sym15040815One-Dimensional Quaternion Fourier Transform with Application to Probability TheoryWahyuni Ekasasmita0Mawardi Bahri1Nasrullah Bachtiar2Amran Rahim3Muhammad Nur4Department of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaDepartment of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaDepartment of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaDepartment of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaDepartment of Mathematics, Hasanuddin University, Makassar 90245, IndonesiaThe Fourier transform occupies a central place in applied mathematics, statistics, computer sciences, and engineering. In this work, we introduce the one-dimensional quaternion Fourier transform, which is a generalization of the Fourier transform. We derive the conjugate symmetry of the one-dimensional quaternion Fourier transform for a real signal. We also collect other properties, such as the derivative and Parseval’s formula. We finally study the application of this transformation in probability theory.https://www.mdpi.com/2073-8994/15/4/815quaternion Fourier transformconvolutionprobability theoryquaternion characteristic function |
| spellingShingle | Wahyuni Ekasasmita Mawardi Bahri Nasrullah Bachtiar Amran Rahim Muhammad Nur One-Dimensional Quaternion Fourier Transform with Application to Probability Theory Symmetry quaternion Fourier transform convolution probability theory quaternion characteristic function |
| title | One-Dimensional Quaternion Fourier Transform with Application to Probability Theory |
| title_full | One-Dimensional Quaternion Fourier Transform with Application to Probability Theory |
| title_fullStr | One-Dimensional Quaternion Fourier Transform with Application to Probability Theory |
| title_full_unstemmed | One-Dimensional Quaternion Fourier Transform with Application to Probability Theory |
| title_short | One-Dimensional Quaternion Fourier Transform with Application to Probability Theory |
| title_sort | one dimensional quaternion fourier transform with application to probability theory |
| topic | quaternion Fourier transform convolution probability theory quaternion characteristic function |
| url | https://www.mdpi.com/2073-8994/15/4/815 |
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